Turbulent dynamo naturally occurs when the turbulent energy exceeds the magnetic energy in astrophysical media,
provided that there is a non-zero seed magnetic field.
The seed field can be of primordial origin
([1]}, [2]}, [3]}, [4]}, [5]}).
The XL16 theory has a broad range of astrophysical applications for studying the evolution and structure of magnetic fields,
e.g., in supernova remnants and the implications on cosmic ray diffusion and acceleration
[6]},
in gravitational collapse and primordial star formation
[7]}, [8]},
and in weakly ionized interstellar phases
[9]}, [10]}.
In this review, we focus on the nonlinear turbulent dynamo (Section 2) and
the dynamo in a partially ionized medium (Section 3) formulated in XL16.
We also provide examples of their applications to studying magnetic field amplification in a variety of
astrophysical processes and astrophysical environments
collected from our recent studies.
